| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 72.1-a2 |
72.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{8} \) |
$1.27520$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.195457709$ |
$20.36069944$ |
1.624687623 |
\( \frac{35168288}{3} a + \frac{86153392}{3} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -23 a - 60\) , \( 70 a + 170\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-23a-60\right){x}+70a+170$ |
| 72.1-d2 |
72.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{8} \) |
$1.27520$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.755738700$ |
1.787257678 |
\( \frac{35168288}{3} a + \frac{86153392}{3} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 20 a - 45\) , \( -53 a + 130\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(20a-45\right){x}-53a+130$ |
| 144.1-b2 |
144.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{8} \) |
$1.51647$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$8.755738700$ |
0.893628839 |
\( \frac{35168288}{3} a + \frac{86153392}{3} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -25 a - 57\) , \( -94 a - 229\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-25a-57\right){x}-94a-229$ |
| 144.1-d2 |
144.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{8} \) |
$1.51647$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$20.36069944$ |
2.078055185 |
\( \frac{35168288}{3} a + \frac{86153392}{3} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 18 a - 48\) , \( 72 a - 177\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(18a-48\right){x}+72a-177$ |
| 600.2-j2 |
600.2-j |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
600.2 |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{6} \) |
$2.16662$ |
$(-a+2), (a+3), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$5.546489528$ |
2.264344867 |
\( \frac{35168288}{3} a + \frac{86153392}{3} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 135 a - 323\) , \( 860 a - 2103\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(135a-323\right){x}+860a-2103$ |
| 600.2-m2 |
600.2-m |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
600.2 |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{6} \) |
$2.16662$ |
$(-a+2), (a+3), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.263247270$ |
$19.28495094$ |
4.145116919 |
\( \frac{35168288}{3} a + \frac{86153392}{3} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -10 a - 26\) , \( 26 a + 60\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-10a-26\right){x}+26a+60$ |
| 600.3-a2 |
600.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
600.3 |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{6} \) |
$2.16662$ |
$(-a+2), (a+3), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$5.546489528$ |
2.264344867 |
\( \frac{35168288}{3} a + \frac{86153392}{3} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -168 a - 412\) , \( -1742 a - 4268\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-168a-412\right){x}-1742a-4268$ |
| 600.3-l2 |
600.3-l |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
600.3 |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{6} \) |
$2.16662$ |
$(-a+2), (a+3), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.133591881$ |
$19.28495094$ |
2.103550661 |
\( \frac{35168288}{3} a + \frac{86153392}{3} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 6 a - 23\) , \( -9 a + 30\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(6a-23\right){x}-9a+30$ |
| 768.1-d2 |
768.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$17.63288296$ |
3.599297162 |
\( \frac{35168288}{3} a + \frac{86153392}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 254 a - 622\) , \( 2336 a - 5722\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(254a-622\right){x}+2336a-5722$ |
| 768.1-e2 |
768.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.294056305$ |
$17.63288296$ |
2.116792049 |
\( \frac{35168288}{3} a + \frac{86153392}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -12\) , \( 12 a + 12\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-12{x}+12a+12$ |
| 768.1-o2 |
768.1-o |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.582692143$ |
1.547810552 |
\( \frac{35168288}{3} a + \frac{86153392}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -12\) , \( -12 a - 12\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-12{x}-12a-12$ |
| 768.1-r2 |
768.1-r |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.288816927$ |
$7.582692143$ |
3.989688880 |
\( \frac{35168288}{3} a + \frac{86153392}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 254 a - 622\) , \( -2336 a + 5722\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(254a-622\right){x}-2336a+5722$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
